1. Field of the Invention
The present invention relates to a birefringence optical element and more particularly to a birefringence optical element with a plurality of trenches arranged at a specified pitch to cause structured birefringence, and a manufacturing method thereof.
2. Description of Related Art
As shown in FIG. 10, when fine structures (trenches) 2 smaller than the wavelength of light L are arranged at a pitch smaller than the wavelength of the light L, the light L does not react to the respective fine structures but reacts to the average refractive index of the fine structures. An area in which this phenomenon appears is referred to as an equivalent refraction area. When fine structures in an equivalent refraction area are positioned to have orientation against an optical surface, the optical surface obtains strong optical anisotropy (polarization A and polarization B in FIG. 10). The optical anisotropy is referred to as structured birefringence.
Birefringence optical elements of this kind are produced conventionally by cutting natural crystal. Recently, however, as disclosed by US 2003/0164534 A1 and Japanese Patent Laid-Open Publication No. 2003-207636, it is suggested that the birefringence optical elements be manufactured from artificial materials.
As FIGS. 10, 11a and 11b show, an example of producing an optical element with structured birefringence is making trenches 2 in a semiconductor substrate 1 at a fine pitch p of about 200 nm at a duty factor of 1:1. The semiconductor substrate 1 with the fine structures formed thereon can be used as an optical element. Also, the semiconductor substrate 1 may be used as a matrix to be printed on a mold to manufacture optical elements by resin molding.
A known method of forming fine structures on a semiconductor substrate at a pitch p of about 200 nm is dry etching or wet etching the semiconductor substrate by use of a mask patterned by photolithography or ion beam lithography.
When an optical element using the birefringence characteristic generated by structured birefringence is used as a polarizer such as a retardation film, the optical element must cause a desired phase difference between longitudinal polarization and horizontal polarization, and light must be propagated within the birefringence medium until the desired phase difference can be obtained.
In a structured birefringence medium, the degree of the phase difference depends on the depth of the trenches. There are cases in which the depth of the trenches must be of several microns depending on the wavelength of light and the material of the medium. In order to make a full usage of the optical characteristics of the medium, the trenches must be formed with extremely high accuracy. For example, if a structural pattern is to be formed at a pitch of 200 nm and at a duty factor of 1:1, trenches with a width of 100 nm and a depth of several microns must be formed, which requires extremely accurate processing. It is difficult to form the trenches with such a depth by dry etching, and a possible way of forming the trenches is anisotropy etching of a semiconductor crystal.
As an example of forming a fine pattern by wet etching, there is a case of forming trenches on a (110) surface of a silicon substrate. Specifically, a mask is patterned such that the side walls of the trenches will be in parallel to a surface perpendicular to the (110) surface, for example, will be in parallel to a combination of mutually opposite surfaces (−111) and (1−1−1) or (1−11) and (−11−1), and wet etching is carried out by use of an alkali solvent such as potassium hydroxide, tetramethyl ammonium hydroxide, etc.
In this case, the etching speed in the (−111) direction and the etching speed in the (1−1−1) direction are lower than the etching speed in the (110) direction, and specifically the etching speeds in the (−111) direction and in the (1−1−1) direction are 1/100 to 1/1000 of the etching speed in the (110) direction. Therefore, it is possible to form good vertical trenches, which are narrow but very deep in the (110) direction.
However, in order to use such a fine structure as an optical element, the structure must have a larger optical area than a bundle of rays (of which diameter is ordinarily, at the minimum, several tens of microns and at the maximum, several centimeters, and may be larger depending on the usage), and very long and narrow trenches must be formed.
In order to form very long trenches, the direction of the mask pattern must be set in a desired direction of the crystal with extremely high accuracy. FIG. 12a shows an opening pattern 5 of a mask, and FIG. 12b shows trenches formed by etching by use of the mask of FIG. 12a. As FIGS. 13a and 13b show, if the mask is placed with the opening pattern 5 displaced from the direction of the crystal even a little (at a displacing angle θ), etching will proceed to reach the (1−11) surface and the (−11−1) surface. Consequently, the widths of the trenches become large, and moreover, adjacent trenches may communicate with each other. In this case, a desired fine periodical structure cannot be obtained.
For example, if the lengths of the trenches 1 mm and if the distance between adjacent trenches is 100 nm, from simple calculation not considering the widths of the trenches (see the expression below), displacement of 6×10−3 degrees will result in connection between adjacent trenches.
  θ  =                    tan                  -          1                    ⁡              (                  100          ⁢                                          ⁢                      nm            /            1                    ⁢                                          ⁢          mm                )              ⁢                  ⁢                  =                                        tan                          -              1                                ⁡                      (                          100              ×                                                10                                      -                    9                                                  /                1                            ×                              10                                  -                  3                                                      )                          ⁢                                  ⁢                                  ≈                              (                          100              ×                                                10                                      -                    9                                                  /                1                            ×                              10                                  -                  3                                                      )                    ⁢          rad                    ⁢                          ⁢                          =                        1          ×                      10                          -              4                                ⁢          rad                ⁢                                  ⁢                                  =                  6          ×                      10                          -              3                                ⁢                                          ⁢          degrees                    
For accurate direction/axis setting, usually, an orientation flat 1a (see FIG. 11a) which is attached to a substrate to indicate the directions of the crystal is used. Even by using the orientation flat 1a, however, it is extremely difficult to set the direction of trenches accurately in the direction of the crystal.